A MeV-Scale Dark QCD Solution to the Axion Domain Wall Problem

Abstract

PQ solution to the strong CP problem probably encounters the axion domain wall problem. In this article, we propose a simple and testable solution, assuming that the $U(1)_{\rm PQ}$ possesses mixed anomaly to a hidden $SU(N_c)$ color. Then, the axion field receives a new cosine potential from the hidden instantons, which breaks the $Z_{N_{\rm DW}}$ subgroup explicitly. The new potential lifts the vacua degeneracy, but also drives the effective $θ$ angle away from the origin, re-incuring the strong CP problem. However, we find that the dark QCD scale within the 0.1 to 3 MeV window survives, maintaining a delicate balance. Two observational signatures are explored: gravitational waves from domain wall collapse, already probed by current PTAs, and di-photon signals from axion-dark-glueball mixing, which require next-generation MeV telescopes. The scenario favors a cold dark QCD sector consistent with dark glueball relic constraints.